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vec(A)=(hat(i)-2hat(j)+6hat(k)) and vec(...

`vec(A)=(hat(i)-2hat(j)+6hat(k))` and `vec(B)=(hat(i)-2hat(j)+hat(k))`, find the cross product between `vec(A)` and `vec(B)`.

Text Solution

AI Generated Solution

To find the cross product of the vectors \(\vec{A}\) and \(\vec{B}\), we will use the determinant method. The vectors are given as: \[ \vec{A} = \hat{i} - 2\hat{j} + 6\hat{k} \] \[ \vec{B} = \hat{i} - 2\hat{j} + \hat{k} \] ...
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vec(A)=(3hat(i)+2hat(j)-6hat(k)) and vec(B)=(hat(i)-2hat(j)+hat(k)) find the scalar product of vec(A) and vec(B) .

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Knowledge Check

  • Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

    A
    Parallel
    B
    Antiparallel
    C
    Perpendicular
    D
    at acute angle with each other

  • vec(A)=hat(j)-2hat(i)+3hat(k) " , "vec(B)= hat(i)+2hat(j)+2hat(k) find vec(A).vec(B)

    A
    3
    B
    6
    C
    -3
    D
    -6

  • If vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k)) then the angle between (vec(a)+vec(b)) and (vec(a)-vec(b)) is

    A
    `(pi)/(3)`
    B
    `(pi)/(4)`
    C
    `(pi)/(2)`
    D
    `(2pi)/(3)`

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    If vec(a)=3hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)-4 hat(j)-3 hat(k) , find |vec(a)-2 vec(b)| .

    If vec(a)=4hat(i)-hat(j)+hat(k) and vec(b)=2hat(i)-2hat(j)+hat(k) , then find a unit vector parallel to the vector vec(a)+vec(b) .

    If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

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    If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+2hat(j)+2hat(k) , find the magnitude of compinent of (vec(A)+vec(B)) along vec(B)

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